Chapter 2.1, Problem 13PSB

To determine

To Prove: $\angle HGK\cong \angle HJK$

Explanation of Solution

Given information: $\angle HGJ={37}^{\circ }20\text{'},\angle HGJ={52}^{\circ }40\text{'}$

  $KJ\perp HJ.$

  

Proof:

Given $KJ\perp HJ.$

Hence $\angle HJK\cong {90}^{\circ }$

Also, $\begin{array}{l}\cong {37}^{\circ }20\text{'}+{52}^{\circ }40\text{'}\\ \cong {90}^{\circ }\end{array}$

  $\therefore \angle HGK\cong \angle HGJ+\angle KGJ$

  $\begin{array}{l}\cong {37}^{\circ }20\text{'}+{52}^{\circ }40\text{'}\\ \cong {90}^{\circ }\end{array}$

  $\angle HGK\cong \angle HJK$